Open your email on a desktop/laptop and find the verification email. You must click the verification link in that email to verify your new email. This completes the email change process in your YouVersion account

It may take up to 6 hrs for your new email address to work as it takes time for it to get to all the sign in servers. Use your username to sign in during that time

After 6 hrs, If you want to prove to yourself that your new email is now associated with your account, sign out then sign in again at https://www.bible.com using your new email and your password. If you are successful in signing in, all is well.